If I have a multivariate function f twice differentiable which is strongly convex, and smooth as well, so $\mathit \nabla ^2f - \mu I$ and $\mathit LI - \nabla ^2 f$ are both positive definite at every point, does the Newton's method to find its minimum always converge ?
Intuitively, I feel like this is true, but I can't find any proof of it.
So far my research did not lead anywhere. The documents I found either focused on finding a root instead of the minimum, or the function used was convex but not strongly.
Thank you for your help